Shape　memory　polymer(SMP)　is　a　class　of　smart　materials　used　in　intelligent　biomedical　devices　and　industrial　application　as　sensors　or　actuators　for　their　ability　to　change　shape　under　a　predetermined　stimulus.　Carbon　nanotube　(CNT)/shape　memory　polymer　(SMP)　composites　demonstrate　good　mechanical　properties　and　shape　memory　effect.　In　this　work,　a　model　of　CNT/SMP　composite　shell　with　a　vaulted　cross-section　was　established.　This　composite　shell　structure　could　further　elevate　the　recovery　stress　of　CNT/SMP　composites.　The　folding　properties　of　CNT/SMP　composite　shell　structure　were　analyzed　by　finite　element　method.,　Furthermore,　the　energy　conservation　principle　were　used　to　study　the　influence　of　structural　parameters　on　the　buckling　behavior　of　the　shell.　The　results　indicate　that　vaulted　cross-section　shell　had　unique　mechanical　properties.　The　structural　parameters,　such　as　the　vaulted　radius　and　the　total　length　have　a　great　impact　on　buckling　moment　of　the　shell.　This　shell　structure　is　expected　to　achieve　effective　control　of　buckling　and　deploying　process,　relying　on　the　special　shape　memory　property　of　SMP　and　high　elastic　modulus　CNTs.　Moreover,　it　could　also　largely　avoid　the　vibration　problem　during　the　deploying　process.